Lightweight construction having a fractally structured supporting structure

ABSTRACT

A lightweight construction includes a superficial surface and a regularly, periodically configured supporting structure that mechanically reinforces the superficial surface. The supporting structure has fractal structuring into at least two fractal planes which have integrated fluid transitions therebetween.

CROSS REFERENCE TO PRIOR APPLICATIONS

This application is a U.S. National Phase application under 35 U.S.C. §371 of International Application No. PCT/DE2008/000287, filed on Feb. 14, 2008 and claims benefit to German Patent Application No. DE 10 2007 011 107.1, filed on Mar. 5, 2007, both of which are hereby incorporated by reference. The International Application was published in German on Sep. 12, 2008 as WO 2008/106925 under PCT Article 21(2).

FIELD

The present invention relates to lightweight constructions whose superficial surface is mechanically reinforced by a supporting structure having a regular, periodic design.

BACKGROUND

Lightweight constructions follow a construction philosophy whose aim is to maximally economize on weight while providing optimal stability. The reasons for lightweight design may vary in nature. A principal argument for lightweight design is raw material savings, both in the manufacturing of the product, as well as in the use thereof When a consistently lightweight design is used for motor vehicles and aircraft, less propulsive power is needed for the same driving or aerodynamic properties. Moreover, the fuel consumption decreases, and the weight ratio between the means of transport and the cargo improves. Thus, the total installation, the engine and the fuel reserve can be dimensioned to be smaller. Lightweight design is very important in vehicle manufacturing, aircraft manufacturing and in aeronautics. In aeronautics, in particular, every kilogram transported costs several thousand euros, so that a lightweight design can provide substantial savings. The lightweight construction method also constitutes a cost-effective and very flexible alternative in building construction, most notably in industry for building production shops, assembly shops and warehouses.

Aluminum, magnesium, high-strength steels and titanium, for example, are metallic, lightweight construction materials. Plastics, wood and paper materials and fiber composite materials are also classic lightweight construction materials. In recent years, plastics and special fiber-plastic composites have gained in importance. Their high specific stiffness and strength make them well suited as lightweight construction materials. They offer an abundance of novel processing and design options.

BACKGROUND INFORMATION

U.S. Patent Application 2002/0108349 A1 describes a plate-shaped lightweight construction having two superficial surfaces between which corrugated or half honeycomb-shaped metal bands extend as reinforcing ribs of a supporting structure. The German Patent Application DE 10 2004 025 667 A1 describes a supporting structure for lightweight constructions having a multilayer design where reinforcing ribs are disposed as closed rectangles in a wall-like, offset configuration and are filled with a filling material. The German Patent Application DE 10 2004 031 823 A1 describes a lightweight construction plate where a plurality of regions of variably corrugated reinforcing ribs are defined. German Patent Application DE 101 19 020 A1 describes curved honeycomb latticeworks having supporting structures of different forms. Supporting structures having a truncated pyramidal configuration in one or more planes are described in German Patent Applications DE 100 22 742 A1, DE 100 37 589 A1 and in German Utility Model Patent DE 203 19 426 U1. The German Patent Application DE 100 37 589 A1 describes a truncated pyramidal supporting structure for a design of lightweight construction in the form of a dome light.

Examined Patent Application EP 0 618 842 B1 describes a honeycomb body having an inner structure held by a supporting structure. The honeycomb body may be configured in a tube. The supporting structure may be composed of superposed corrugated sheet-metal sections having different radii. A lightweight hollow-body structural component is described in the German Patent Application DE 198 48 516 A1. The tub-shaped lightweight construction has an interior space. The supporting structure made of reinforcing ribs extending in a grid form is disposed in the wall between the two surfaces.

German Patent Application DE 100 47 753 A1 describes a lightweight construction having a regularly, periodically designed supporting structure that mechanically reinforces its superficial surface. The supporting structure is composed of reinforcing ribs configured in a star pattern. The lightweight construction has a tubular design and includes a useful interior space. The supporting structure is configured on the exterior of the tube between an inner superficial surface and an outer superficial surface which serves as an outer skin. Relatively small wall thicknesses can be used for the outer skin, the inner skin, and for the reinforcing ribs, a very lightweight construction being thereby obtained which, nevertheless, exhibits high strength due to the complex supporting structure. However, the notch effect subjects the known supporting structure to high mechanical loads and thus to stress peaks at the acute-angled intersecting points of the reinforcing ribs. Moreover, triangular regions having no further support are disposed between the individual reinforcing ribs, so that these locations must not be subject to greater pressure forces. This could only be remedied by increasing the wall and reinforcing-rib thicknesses, which, however, is not consistent with material savings in lightweight constructions.

SUMMARY

In an embodiment, the present invention provides a lightweight construction including a superficial surface and a regularly, periodically configured supporting structure that mechanically reinforces the superficial surface. The supporting structure has fractal structuring into at least two fractal planes which have integrated fluid transitions therebetween.

BRIEF DESCRIPTION OF THE DRAWINGS

Examples of a lightweight construction having a fractal supporting structure according to the present invention are presented in the following with reference to the following thirteen figures. Other features and advantages of the various embodiments of the light weight construction according to the present invention will become apparent by reading the following detailed description with reference to the attached drawings which illustrate the following:

FIG. 1 is a photograph of plan view of a shell of an ammonite having suture lines;

FIG. 2 is a photograph of a view into the shell of the ammonite in accordance with FIG. 1;

FIG. 3 is a diagram for developing ever more complex suture lines;

FIG. 4 illustrates simulations of various suture lines according to the prior art;

FIG. 5 is a photograph of a view into a shell of another ammonite;

FIG. 6 illustrates a fractal supporting structure;

FIG. 7 illustrates a halved longitudinal section of the supporting structure according to FIG. 6 in a tube;

FIG. 8 illustrates a second fractal supporting structure;

FIG. 9 illustrates a housing having a third fractal supporting structure in honeycomb form;

FIG. 10, 11, 12 are microscopic images of microalgae; and

FIG. 13 illustrates the evolutionary development of ammonites having simulated stress diagrams.

DETAILED DESCRIPTION

To attain a lightweight design, structural design measures are employed in lightweight constructional design. The aim, first and foremost, is a most uniform possible utilization of the material volume. Thus, for example, components subject to flexural stress are replaced by sandwich-type designs or latticeworks. Efforts are directed, in principle, to providing the most thin-walled constructions possible. However, this increases the danger of stability breakdown (buckling, bending), thereby necessitating a precise mechanical analysis. In lightweight constructions, forces should be transmitted directly. In complex constructions, notch stresses, in particular, must be minimized. Along these lines, lattice frames having pure tension and pressure bars constitute optimal structures.

Starting out, for example, from the lightweight construction of the type described having a regularly, periodically designed supporting structure of reinforcing ribs that mechanically reinforces its superficial surface in accordance with, for example, the German

Patent Application DE 100 47 753 A1, an embodiment of the present invention provides a lightweight construction in such a way that both a material savings as well as an enhanced system reliability are achieved in connection with the parameter “pressure resistance of hollow bodies and sealing and coupling elements.” The combination of the parameters system reliability, material savings and pressure resistance is of particular importance, for example, for lightweight constructions for airplanes, ships' hulls and submersibles, as well as, for example, for aircraft bulkheads and dome lights.

The lightweight construction according to an embodiment of the present invention may be described as a fractal structuring of the supporting structure into at least two fractal planes whereby the configuration of the supporting contour is repeated in itself at least one further time. The number of self-similar repetitions that become smaller by one dimension is given as a function of the number of fractal planes. Among the planes, the transitions are fluid and integrated. Advantages associated with the use of a fractal supporting structure are that notch stress peaks are reliably prevented by the direct, fluid transitions (in the Z direction) among the integrated structures in the various fractal planes of the supporting structure not having any notch or fracture edges, and that, given the same strength, lighter structures, which provide more effective supporting action, may be used. The strength is derived from the proper formation of the fractal supporting structure, both in small support regions, as well as in relatively large support regions and in fairly large support regions. Thus, the structuring of the supporting structure increases with the size of the support region and is able to be readily adapted thereto. Moreover, the structure may be fabricated from a casting material, thereby eliminating the need for special connections or adhesive bonds and ruling out the problems associated therewith. The present invention applies a principle not employed under known methods heretofore of a fractally structured peripheral region having integrated fluid transitions disposed perpendicularly to the superficial surface (Z direction) to support superficial surfaces.

The term “fractal” (adjective or noun) was coined by Benoit Mandelbrot (1975) and is derived from the Latin word ‘fractus’ meaning ‘broken.’ Fractals denote natural or artificial formations or geometric patterns which exhibit a high degree of scale invariance or self-similarity. This is the case, for example, when an object is composed of a plurality of reduced-scale copies of itself. Each reduction in size then defines a fractal plane. Observed throughout is the fluid transition between the structural elements in the various fractal planes. Geometric objects of this type differ in important aspects from ordinary smooth figures. However, the self-similarity does not need to be perfect, as exhibited by the successful application of the fractal geometry methods to natural formations such as trees, clouds, coastlines, etc. The mentioned objects are self-similarly structured to a greater or lesser degree (a tree branch roughly resembles a tree on a smaller scale). However, the similarity is not strict, but rather stochastic. In contrast to shapes of Euclidian geometry, which, when enlarged, often become flatter and flatter and thus simpler (for example, a circle), in the case of fractals, ever more complex and new details appear.

Fractal patterns are often generated by recursive operations. Even simple generating rules produce complex patterns following a few recursive steps. This is evident in the example of a Pythagoras tree. Such a tree is a fractal which is constructed from squares that are arranged in a configuration as defined by the pythagorean theorem. Another fractal is the Newton fractal. It is calculated by applying Newton's method for calculating zero points. A fractal in three-dimensional space is the Menger sponge. Fractal concepts are also found in nature. In this context, however, the number of planes of self-similar structures is limited and is often only 3-5. Typical examples from biology are the strictly fractal structures that occur in the cultivation of the green cauliflower, romanesco, in ferns and in ammonites. The book “Ammonoideen: Leben zwischen Skylla and Charybdis” by Ulrich Lehmann (Enke Publishers, Stuttgart 1990), pp. 63-105, provides a good overview of fractal structures in ammonites. However, microalgae also often exhibit fractally constructed supporting structures in a plurality of planes. Fractal structures having statistical self-similarity are also widespread. These include trees, the blood circuit, river systems and coastlines.

Until now, protective rights on the subject of “fractal design” are only known from antenna manufacturing (German Examined Application DE 10 2004 013 642 B4, World Patent Application PCT, transfer to DE 696 33 975 T2), from the production of a damping structure in the peripheral region of a circuit board (German Patent Application DE 103 36 290 A1), from interfluid turbulence (World Patent Application PCT, transfer to DE 697 31 841 T2) or polymers (World Patent Application PCT, transfer to DE 696 35 552 T2), and from a partial street cover used for noise protection (German Patent Application DE 102 20 989 A1). Fractal supporting structures having a form modeled after ammonites or microalgae, in particular kiesel algae shells, are not described in technical applications.

The highly specialized ammonites (Latin Ammonoidea), which existed in a great variety of forms, died out in connection with a global natural disaster (meteorite impact) approximately 65 million years ago. Nevertheless, their structural features were much more highly developed than those of their relatives living today, such as Nautilus, for example. Therefore, some of the structures that are most interesting for lightweight designs are not to be sought in the present, but rather, as in the case illustrated here, in the Cretaceous period. Over the course of evolution, dividing walls (septa) of the gas-filled shell portion (phragmocon) had a tendency to form ever more filigreed and complex foldings, so that, for numerous ammonites of the Cretaceous period, for example, every square centimeter of the outer skin is supported by the inner structures. Toward the middle of the dividing wall, their highly folded outer regions join to form a simple, smooth surface and show the integrated fluid transitions between the structural elements in the individual fractal planes which lead to a virtually perfect freedom from notch stresses. An embodiment of the fractally structured supporting structure according to the present invention may be practical when the interior space of lightweight construction is or is not completely intended for one use (for example, bumpers, ships' decks, ships' hulls and airplane parts for storing liquids (fuels, thus tankers and airfoils)). In this context, depending on the requirement and spatial conditions, the supporting structures may be provided both on the outside, as well as on the inside of the superficial surface. Constructions that are to be built to be particularly stable may also have supporting structures on both sides of the outer skin. A supporting structure may have an exceptionally variable design and, on the other hand, be adapted to load and space conditions.

An element that frequently occurs in a supporting structure is the reinforcing rib. Other elements include supporting arches, supporting bridges, supporting struts, supporting columns, supporting walls and supporting plates. One can also speak in this context in connection with an embodiment of the present invention then in generalized terms of reinforcing ribs when they extend, for example, in the interior space of a tube over the entire cross section thereof. Reinforcing ribs are typically known from construction engineering as not having a continuous, integrated design. In this context, the reinforcing ribs forming a type of dividing wall (analogously to the septa of the ammonites) in no way need to have an impervious form; rather, they may absolutely be provided, as needed, with single or multiple openings to allow the passage of fluids. Depending on the type of lightweight construction, the supporting structure may be fabricated from a broad array of materials, for example, from wood, cardboard, plastics, fiber and other composite materials and from metal materials. At the present time, a complete overview of the fields of application of the present invention for the industry is not yet possible. Countless fields of application are conceivable: beginning with weight savings for supertankers, which would then be able to transport more freight; spanning submarines submersible to greater depths, lighter airfoils and airplane fuselages, bumpers and side-impact protection of vehicles; all the way to new designs for seating furniture. A specific example of an application is also the air bulkhead of airplanes, which, comparably to the outermost dividing wall of the ammonites, is subject to a distinct pressure difference.

In accordance with the model found in nature, the fractal form of the reinforcing ribs may also have a meander-shaped configuration of the reinforcing ribs superposed thereon, thereby providing an especially uniform supporting of the superficial surface. Meander shapes are understood in the context of an embodiment of the present invention not as being orthogonal, but rather as rounded forms featuring changes in direction in the characteristic line formations, thus in the sense of undulations. In this context, the meander-shaped configuration may also be asymmetrical. When it comes to the ammonites, it is, namely, apparent that the outer, meandering regions of the supporting structures (the suture lines) are typically asymmetrically configured, i.e., acute in one direction and arcuate in the other. From a technical standpoint, this is useful in the case of a pressure difference between two chambers separated by these structures when the maximum tensile strength of the material significantly differs from the pressure resistance.

Moreover, the reinforcing ribs may also extend in a closed form, for example, as a square- or preferably honeycomb-shaped structure. The fractal form is then derived from the integrated configuration of honeycomb reinforcing ribs that become ever smaller and lower. It is brought to bear in this context that the surface pressure and the material cross section both scale to the square of the linear scale. Therefore, the width and height of the honeycomb structures are scaled down to the same degree as the diameter thereof. Using this approach, the outer skins of pressure housings may be formed to any desired thinness as a function of the number of fractal planes. The integrated honeycombs may be applied both on the interior as well as on the exterior. Each fractal plane is defined by a small-scale form of the supporting structure. It is likewise advantageously possible to combine the fractal supporting structure with a non-fractal, conventional supporting structure, for example, a simple rib structure.

In addition, the superficial surface of the lightweight construction may take the form of outer skin. It may be a question then, for example, of an airfoil or a bulkhead of an airplane or of a ship's hull. Lightweight constructions of this kind, which are more likely to be plate-shaped in design, but in some instances are formed with a curvature, typically have a useful interior space. Therefore, the supporting structure is not able to traverse the entire interior space, but rather may only be configured in the region of the outer skin. The interior space may also be a tube. In this case, the supporting structure may preferably be configured in the tube. The reinforcing ribs may then traverse the entire tube and include recesses if a fluid is to flow within the tube. The fractally extending reinforcing ribs may preferably be formed as an axially coiled radial plane or as a plurality of planar radial planes.

FIG. 1 shows the suture lines of an ammonite (Amphipopanoceras medium) on a steinkern of a phosphatized specimen having calcite filling found on Spitsbergen. The suture line represents the line of contact of the inner supporting structure, respectively of the reinforcing ribs (septa) with the outer shell wall. Clearly discernible is the fractally structured form of the suture lines. However, this folding is only limited to the peripheral region; toward the inner portion, the form smooths out (compare FIG. 2) and exhibits the integrated fluid transitions between the fractal planes. Thus, the fractal structuring acts to optimally support the thin outer skin.

The outer walls of the gas-filled chambers were not able to be repaired by the animal because they did not extend to living tissue. Thus, damage to the chamber walls and the flooding of the chambers associated therewith led to the uncontrolled sinking of the animal and thus to its death. For that reason, it is practical from a standpoint of historical development that the ammonites developed ever more stable shells in that animals having these more stable shells survived attacks by predators or were able to take advantage of food resources located at greater depths and not reachable by others. In this context, two circumstances hindered the development of more massive solid shells. First of all, a more massive shell having thicker walls requires a greater degree of complexity for construction. Additional energy would have to be invested to construct the shell and would then be lacking for other areas vital to life. On the other hand, thicker housing walls also signify additional weight, which, in the case of an animal that moves by floating in the water, can only be compensated within narrow limits.

Thus, animals who succeeded in developing a more stable shell without using more material for that purpose had the best chances to survive and reproduce. Similarly, a trend repeatedly evident in the developmental history of the ammonites was the formation of fractally folded septa structures. Over time, the dividing walls between the chambers became ever more filigreed and complex (see FIG. 3). The repeated formation of this very special septa form reveals that this is not a random development; rather, folded chamber walls provide a considerable competitive advantage. In principle, the ammonite septum had to fulfill two functions. It strengthened the shell against attack by predators who attempted to break open the shell using their teeth. This was a violent punctiform load. The second function of the septum was stabilizing the shell against an elevated outside pressure, as occurs at great depths. A uniform compressive load occurred in the process at the periphery of the shell and at the septum at the end of the living chamber.

Over the course of developmental history of the ammonites, this animal group was brought several times to the verge of total extinction. These periods of drastic decline in the biodiversity of the ammonites mostly coincided with the transition from one era to the next. Often, only one or two not very specialized species having a simple shell design survived. During subsequent reproduction of the species, a more pronounced folding of the septa again occurred.

FIG. 4 shows various simulations of ammonite septa (above left: by corrugated sheet; above right: by wire loop and soap bubble; bottom left: by wire loop and paper; bottom right: by wire loop and rubber skin). The fractal supporting structure is clearly discernible in a plurality of fractal planes. It is also clearly discernible that the shape of the supporting structures is configured in response to a lateral compressive stress—via the outer housing wall.

FIG. 5 shows a fractally structured supporting structure having a treelike pattern (found in Lytoceras siemensi).

In a 1.5-fold magnification, FIG. 6 shows a detail from a first fractally structured (or in shortened form: fractal) supporting structure FSS1 for placement in a tube. Reinforcing ribs SR extend on the one side S1 in a superordinated, high-level wave form WV11 and are undulated a second time within this superordinated wave form WV11, so that a subordinate, secondary wave form WV12 approximately having an order of magnitude of dimensions smaller than the superordinated wave form WV11 thereby results. The superordinated wave form WV11 forms a first fractal plane FE1; the subordinate wave form WV12 forms a second fractal plane FE2. The transition between the two fractal planes FE1, FE2 is fluidly integrated, so that no acute notches and thus no notch stress peaks occur. This is shown clearly again in the smoothing of supporting structure FSS1 toward the axial center. If subordinate wave form WV12 were to again be undulated in its characteristic form, then a third fractal plane would also be present. Analogously, reinforcing ribs SR on other side S2 extend in a superordinated wave form WV21 and in a subordinated wave form WV22. Here, however, the distinction is that the period of superordinated wave form WV21 is offset by one half period from superordinated wave form WV11 on first side S1, so that, on first side S1, the wave maxima oppose the wave minima on second side S2.

In the original scale, FIG. 7 shows fractally structured supporting structure FSS1 in the configuration in a lengthwise, cut-away view of tube RO. It is clearly discernible that fractally structured supporting structure FSS1 again has fluid, integrated transitions in the direction of the tube axis and optimally supports tube RO on the inner side thereof Tube RO has a usable interior space NI through which fluid may flow, for example. To that end, support ribs SR have a plurality of openings DB. The superficial surface of tube RO may be conceived as outer skin AH and thus be subject to environmental influences, in particular also compressive loads. Tube RO represents a lightweight construction LBK since, instead of a thick, material-intensive wall, it features a filigreed, fractally structured supporting structure FSS1.

In a two-fold magnification, FIG. 8 shows a second fractal supporting structure FSS2 in a halved longitudinal section which corresponds to first fractally structured supporting structure FSS1, but has a different period.

FIG. 9 shows a housing GH having a fractally structured supporting structure FSS3 in honeycomb form. Fractally structured supporting structure FSS3 has two fractal planes: a first fractal plane FE1 having individual honeycombs WB1; located within each honeycomb WB1 are five increasingly smaller honeycombs WB2 that form second fractal plane FE2. Other honeycombs within these small honeycombs would form a third fractal plane.

It is also discernible in FIG. 9 that fractally structured supporting structure FSS3 is superposed by another non-fractal supporting structure NFS (in this case, however, outside of supporting structure FSS3; a direct superposition of the structures is likewise possible). This is a question of a simple, linear rib structure having a longitudinal rib LR and a plurality of transverse ribs QR. By combining various supporting structures FSS, NFS of the fractal and non-fractal type, any lightweight construction may be optimally stiffened without necessitating any significant increase in the amount of material used.

The model found in nature for the fractally structured supporting structure FSS3 in accordance with FIG. 9 is shown in FIG. 10: These microalgae in the form of benthic kiesel algae show a fractal structuring into three fractal planes. FIG. 11 shows another very striking, fractally structured kiesel algae shell. FIG. 12 shows a fractally structured kiesel algae (Isthmia) having a non-fractal rib structure that directly superposes the fractal structuring.

In the upper portion, FIG. 13 shows the evolution of an ammonite exhibiting increasing complexity of the supporting structure. The ammonite on the right shows a fractal supporting structure. The corresponding stress diagrams (prepared in accordance with the finite element method FEM) show an enhanced performance in the region of the outer skin due to the fractal structuring (the core region of intense stresses (dark coloration) has become smaller; the entire region of the stress application (light gray coloration) has become larger and thus more uniform).

While the invention has been described with reference to particular embodiments thereof, it will be understood by those having ordinary skill the art that various changes may be made therein without departing from the scope and spirit of the invention. Further, the present invention is not limited to the embodiments described herein; reference should be had to the appended claims.

REFERENCE NUMERAL LIST

AH outer skin

DB opening

FE fractal plane

FSS fractally structured supporting structure

GH housing

LBK lightweight construction

LR longitudinal rib

NFS non-fractal supporting structure

NI usable interior space

QR transverse rib

RO tube

S side

SR reinforcing rib

WB honeycomb

WV wave form 

1-16. (canceled)
 17. A lightweight construction comprising: a superficial surface; and a regularly, periodically configured supporting structure that mechanically reinforces the superficial surface, the supporting structure having fractal structuring into at least two fractal planes having integrated fluid transitions therebetween.
 18. The lightweight construction according to claim 17, wherein the supporting structure is disposed on at least one of an outside and an inside of the superficial surface.
 19. The lightweight construction according to claim 17, wherein the supporting structure includes reinforcing ribs having a fractal form.
 20. The lightweight construction according to claim 19, wherein the fractal form of the reinforcing ribs corresponds to at least one of a model of ammonites and a model of microalgae.
 21. The lightweight construction according to claim 19, wherein the supporting structure includes a superposition of the fractally extending reinforcing ribs by a meander-shaped configuration of the reinforcing ribs.
 22. The lightweight construction according to claim 21, wherein the reinforcing ribs have an asymmetrical, meander-shaped configuration.
 23. The lightweight construction according to claim 19, wherein the reinforcing ribs have a closed configuration.
 24. The lightweight construction according to claim 23, wherein the reinforcing ribs are configured in a honeycomb-shaped configuration.
 25. The lightweight construction according to claim 17, wherein the supporting structure has a combination of the fractal structuring with a non-fractally structured supporting structure.
 26. The lightweight construction according to claim 17, wherein at least one opening is disposed in the supporting structure so as to provide for a passage of fluids.
 27. The lightweight construction according to claim 17, wherein the superficial surface is configured as an outer skin.
 28. The lightweight construction according to claim 17, wherein a useful interior space is provided.
 29. The lightweight construction according to claim 27, wherein the outer skin has a form of a tube.
 30. The lightweight construction according to claim 29, wherein the supporting structure is disposed in the tube and includes a superposition of fractally extending reinforcing ribs having a configuration of at least one of an axially coiled radial plane and a plurality of planar radial planes.
 31. The lightweight construction according to claim 17, wherein the lightweight construction has a plate-shaped formation.
 32. The lightweight construction according to claim 31, wherein the plate shaped formation includes a pressure-resistant bulkhead. 